Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,11,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(27.3203618650\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.19 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.11.b.b.42.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.51570i | 0.172366i | 0.996279 | + | 0.0861828i | \(0.0274669\pi\) | ||||
−0.996279 | + | 0.0861828i | \(0.972533\pi\) | |||||||
\(3\) | 292.852i | 1.20515i | 0.798061 | + | 0.602577i | \(0.205859\pi\) | ||||
−0.798061 | + | 0.602577i | \(0.794141\pi\) | |||||||
\(4\) | 993.577 | 0.970290 | ||||||||
\(5\) | − | 3204.10i | − | 1.02531i | −0.858594 | − | 0.512656i | \(-0.828661\pi\) | ||
0.858594 | − | 0.512656i | \(-0.171339\pi\) | |||||||
\(6\) | −1615.28 | −0.207727 | ||||||||
\(7\) | 16511.8i | 0.982434i | 0.871037 | + | 0.491217i | \(0.163448\pi\) | ||||
−0.871037 | + | 0.491217i | \(0.836552\pi\) | |||||||
\(8\) | 11128.3i | 0.339610i | ||||||||
\(9\) | −26713.4 | −0.452394 | ||||||||
\(10\) | 17672.9 | 0.176729 | ||||||||
\(11\) | 31573.6 | 0.196047 | 0.0980235 | − | 0.995184i | \(-0.468748\pi\) | ||||
0.0980235 | + | 0.995184i | \(0.468748\pi\) | |||||||
\(12\) | 290971.i | 1.16935i | ||||||||
\(13\) | 240071. | 0.646582 | 0.323291 | − | 0.946300i | \(-0.395211\pi\) | ||||
0.323291 | + | 0.946300i | \(0.395211\pi\) | |||||||
\(14\) | −91074.0 | −0.169338 | ||||||||
\(15\) | 938328. | 1.23566 | ||||||||
\(16\) | 956042. | 0.911753 | ||||||||
\(17\) | 1.02720e6 | 0.723454 | 0.361727 | − | 0.932284i | \(-0.382187\pi\) | ||||
0.361727 | + | 0.932284i | \(0.382187\pi\) | |||||||
\(18\) | − | 147343.i | − | 0.0779771i | ||||||
\(19\) | 1.67184e6i | 0.675192i | 0.941291 | + | 0.337596i | \(0.109614\pi\) | ||||
−0.941291 | + | 0.337596i | \(0.890386\pi\) | |||||||
\(20\) | − | 3.18352e6i | − | 0.994851i | ||||||
\(21\) | −4.83551e6 | −1.18398 | ||||||||
\(22\) | 174150.i | 0.0337918i | ||||||||
\(23\) | −6.08630e6 | −0.945615 | −0.472807 | − | 0.881166i | \(-0.656759\pi\) | ||||
−0.472807 | + | 0.881166i | \(0.656759\pi\) | |||||||
\(24\) | −3.25896e6 | −0.409282 | ||||||||
\(25\) | −500648. | −0.0512663 | ||||||||
\(26\) | 1.32416e6i | 0.111448i | ||||||||
\(27\) | 9.46955e6i | 0.659949i | ||||||||
\(28\) | 1.64057e7i | 0.953246i | ||||||||
\(29\) | 1.23237e7i | 0.600828i | 0.953809 | + | 0.300414i | \(0.0971248\pi\) | ||||
−0.953809 | + | 0.300414i | \(0.902875\pi\) | |||||||
\(30\) | 5.17554e6i | 0.212985i | ||||||||
\(31\) | −5.08085e6 | −0.177471 | −0.0887357 | − | 0.996055i | \(-0.528283\pi\) | ||||
−0.0887357 | + | 0.996055i | \(0.528283\pi\) | |||||||
\(32\) | 1.66687e7i | 0.496765i | ||||||||
\(33\) | 9.24639e6i | 0.236267i | ||||||||
\(34\) | 5.66573e6i | 0.124699i | ||||||||
\(35\) | 5.29054e7 | 1.00730 | ||||||||
\(36\) | −2.65418e7 | −0.438953 | ||||||||
\(37\) | 2.30677e7i | 0.332656i | 0.986071 | + | 0.166328i | \(0.0531910\pi\) | ||||
−0.986071 | + | 0.166328i | \(0.946809\pi\) | |||||||
\(38\) | −9.22138e6 | −0.116380 | ||||||||
\(39\) | 7.03054e7i | 0.779230i | ||||||||
\(40\) | 3.56564e7 | 0.348207 | ||||||||
\(41\) | −7.74946e7 | −0.668886 | −0.334443 | − | 0.942416i | \(-0.608548\pi\) | ||||
−0.334443 | + | 0.942416i | \(0.608548\pi\) | |||||||
\(42\) | − | 2.66712e7i | − | 0.204078i | ||||||
\(43\) | 2.90004e7 | + | 1.44120e8i | 0.197270 | + | 0.980349i | ||||
\(44\) | 3.13708e7 | 0.190223 | ||||||||
\(45\) | 8.55925e7i | 0.463845i | ||||||||
\(46\) | − | 3.35702e7i | − | 0.162991i | ||||||
\(47\) | −2.22341e8 | −0.969460 | −0.484730 | − | 0.874664i | \(-0.661082\pi\) | ||||
−0.484730 | + | 0.874664i | \(0.661082\pi\) | |||||||
\(48\) | 2.79979e8i | 1.09880i | ||||||||
\(49\) | 9.83663e6 | 0.0348230 | ||||||||
\(50\) | − | 2.76142e6i | − | 0.00883655i | ||||||
\(51\) | 3.00818e8i | 0.871873i | ||||||||
\(52\) | 2.38529e8 | 0.627372 | ||||||||
\(53\) | −1.87870e8 | −0.449240 | −0.224620 | − | 0.974446i | \(-0.572114\pi\) | ||||
−0.224620 | + | 0.974446i | \(0.572114\pi\) | |||||||
\(54\) | −5.22312e7 | −0.113753 | ||||||||
\(55\) | − | 1.01165e8i | − | 0.201010i | ||||||
\(56\) | −1.83749e8 | −0.333645 | ||||||||
\(57\) | −4.89603e8 | −0.813710 | ||||||||
\(58\) | −6.79736e7 | −0.103562 | ||||||||
\(59\) | −5.73654e8 | −0.802398 | −0.401199 | − | 0.915991i | \(-0.631406\pi\) | ||||
−0.401199 | + | 0.915991i | \(0.631406\pi\) | |||||||
\(60\) | 9.32302e8 | 1.19895 | ||||||||
\(61\) | 4.87066e7i | 0.0576685i | 0.999584 | + | 0.0288343i | \(0.00917950\pi\) | ||||
−0.999584 | + | 0.0288343i | \(0.990820\pi\) | |||||||
\(62\) | − | 2.80245e7i | − | 0.0305900i | ||||||
\(63\) | − | 4.41086e8i | − | 0.444447i | ||||||
\(64\) | 8.87048e8 | 0.826128 | ||||||||
\(65\) | − | 7.69213e8i | − | 0.662948i | ||||||
\(66\) | −5.10003e7 | −0.0407243 | ||||||||
\(67\) | 6.11603e8 | 0.452997 | 0.226499 | − | 0.974012i | \(-0.427272\pi\) | ||||
0.226499 | + | 0.974012i | \(0.427272\pi\) | |||||||
\(68\) | 1.02060e9 | 0.701960 | ||||||||
\(69\) | − | 1.78239e9i | − | 1.13961i | ||||||
\(70\) | 2.91810e8i | 0.173624i | ||||||||
\(71\) | − | 2.16541e9i | − | 1.20019i | −0.799930 | − | 0.600094i | \(-0.795130\pi\) | ||
0.799930 | − | 0.600094i | \(-0.204870\pi\) | |||||||
\(72\) | − | 2.97276e8i | − | 0.153638i | ||||||
\(73\) | 5.90470e8i | 0.284828i | 0.989807 | + | 0.142414i | \(0.0454865\pi\) | ||||
−0.989807 | + | 0.142414i | \(0.954514\pi\) | |||||||
\(74\) | −1.27234e8 | −0.0573384 | ||||||||
\(75\) | − | 1.46616e8i | − | 0.0617838i | ||||||
\(76\) | 1.66110e9i | 0.655132i | ||||||||
\(77\) | 5.21336e8i | 0.192603i | ||||||||
\(78\) | −3.87783e8 | −0.134312 | ||||||||
\(79\) | 3.70326e9 | 1.20351 | 0.601753 | − | 0.798682i | \(-0.294469\pi\) | ||||
0.601753 | + | 0.798682i | \(0.294469\pi\) | |||||||
\(80\) | − | 3.06326e9i | − | 0.934832i | ||||||
\(81\) | −4.35058e9 | −1.24773 | ||||||||
\(82\) | − | 4.27437e8i | − | 0.115293i | ||||||
\(83\) | 4.86372e9 | 1.23475 | 0.617374 | − | 0.786670i | \(-0.288196\pi\) | ||||
0.617374 | + | 0.786670i | \(0.288196\pi\) | |||||||
\(84\) | −4.80445e9 | −1.14881 | ||||||||
\(85\) | − | 3.29126e9i | − | 0.741767i | ||||||
\(86\) | −7.94920e8 | + | 1.59958e8i | −0.168978 | + | 0.0340026i | ||||
\(87\) | −3.60901e9 | −0.724089 | ||||||||
\(88\) | 3.51362e8i | 0.0665796i | ||||||||
\(89\) | − | 6.61537e9i | − | 1.18469i | −0.805685 | − | 0.592345i | \(-0.798202\pi\) | ||
0.805685 | − | 0.592345i | \(-0.201798\pi\) | |||||||
\(90\) | −4.72102e8 | −0.0799510 | ||||||||
\(91\) | 3.96400e9i | 0.635224i | ||||||||
\(92\) | −6.04721e9 | −0.917521 | ||||||||
\(93\) | − | 1.48794e9i | − | 0.213880i | ||||||
\(94\) | − | 1.22637e9i | − | 0.167102i | ||||||
\(95\) | 5.35675e9 | 0.692283 | ||||||||
\(96\) | −4.88146e9 | −0.598678 | ||||||||
\(97\) | 3.91240e9 | 0.455601 | 0.227800 | − | 0.973708i | \(-0.426847\pi\) | ||||
0.227800 | + | 0.973708i | \(0.426847\pi\) | |||||||
\(98\) | 5.42559e7i | 0.00600228i | ||||||||
\(99\) | −8.43438e8 | −0.0886905 | ||||||||
\(100\) | −4.97432e8 | −0.0497432 | ||||||||
\(101\) | 3.04443e9 | 0.289667 | 0.144834 | − | 0.989456i | \(-0.453735\pi\) | ||||
0.144834 | + | 0.989456i | \(0.453735\pi\) | |||||||
\(102\) | −1.65922e9 | −0.150281 | ||||||||
\(103\) | 1.78627e10 | 1.54085 | 0.770424 | − | 0.637532i | \(-0.220045\pi\) | ||||
0.770424 | + | 0.637532i | \(0.220045\pi\) | |||||||
\(104\) | 2.67160e9i | 0.219586i | ||||||||
\(105\) | 1.54935e10i | 1.21395i | ||||||||
\(106\) | − | 1.03624e9i | − | 0.0774336i | ||||||
\(107\) | 2.44008e10 | 1.73974 | 0.869871 | − | 0.493279i | \(-0.164202\pi\) | ||||
0.869871 | + | 0.493279i | \(0.164202\pi\) | |||||||
\(108\) | 9.40873e9i | 0.640342i | ||||||||
\(109\) | −1.37165e10 | −0.891478 | −0.445739 | − | 0.895163i | \(-0.647059\pi\) | ||||
−0.445739 | + | 0.895163i | \(0.647059\pi\) | |||||||
\(110\) | 5.57996e8 | 0.0346471 | ||||||||
\(111\) | −6.75541e9 | −0.400901 | ||||||||
\(112\) | 1.57860e10i | 0.895737i | ||||||||
\(113\) | 6.06915e9i | 0.329409i | 0.986343 | + | 0.164705i | \(0.0526671\pi\) | ||||
−0.986343 | + | 0.164705i | \(0.947333\pi\) | |||||||
\(114\) | − | 2.70050e9i | − | 0.140256i | ||||||
\(115\) | 1.95011e10i | 0.969551i | ||||||||
\(116\) | 1.22445e10i | 0.582977i | ||||||||
\(117\) | −6.41312e9 | −0.292509 | ||||||||
\(118\) | − | 3.16410e9i | − | 0.138306i | ||||||
\(119\) | 1.69609e10i | 0.710746i | ||||||||
\(120\) | 1.04420e10i | 0.419642i | ||||||||
\(121\) | −2.49405e10 | −0.961566 | ||||||||
\(122\) | −2.68651e8 | −0.00994007 | ||||||||
\(123\) | − | 2.26944e10i | − | 0.806110i | ||||||
\(124\) | −5.04822e9 | −0.172199 | ||||||||
\(125\) | − | 2.96859e10i | − | 0.972749i | ||||||
\(126\) | 2.43290e9 | 0.0766074 | ||||||||
\(127\) | −3.99008e10 | −1.20771 | −0.603855 | − | 0.797094i | \(-0.706369\pi\) | ||||
−0.603855 | + | 0.797094i | \(0.706369\pi\) | |||||||
\(128\) | 2.19614e10i | 0.639161i | ||||||||
\(129\) | −4.22057e10 | + | 8.49283e9i | −1.18147 | + | 0.237741i | ||||
\(130\) | 4.24275e9 | 0.114269 | ||||||||
\(131\) | − | 4.31876e10i | − | 1.11944i | −0.828680 | − | 0.559722i | \(-0.810908\pi\) | ||
0.828680 | − | 0.559722i | \(-0.189092\pi\) | |||||||
\(132\) | 9.18700e9i | 0.229247i | ||||||||
\(133\) | −2.76051e10 | −0.663332 | ||||||||
\(134\) | 3.37342e9i | 0.0780811i | ||||||||
\(135\) | 3.03414e10 | 0.676654 | ||||||||
\(136\) | 1.14311e10i | 0.245692i | ||||||||
\(137\) | − | 7.78479e9i | − | 0.161304i | −0.996742 | − | 0.0806518i | \(-0.974300\pi\) | ||
0.996742 | − | 0.0806518i | \(-0.0257002\pi\) | |||||||
\(138\) | 9.83111e9 | 0.196430 | ||||||||
\(139\) | 7.64081e10 | 1.47253 | 0.736267 | − | 0.676691i | \(-0.236587\pi\) | ||||
0.736267 | + | 0.676691i | \(0.236587\pi\) | |||||||
\(140\) | 5.25656e10 | 0.977376 | ||||||||
\(141\) | − | 6.51130e10i | − | 1.16835i | ||||||
\(142\) | 1.19438e10 | 0.206871 | ||||||||
\(143\) | 7.57991e9 | 0.126760 | ||||||||
\(144\) | −2.55391e10 | −0.412471 | ||||||||
\(145\) | 3.94863e10 | 0.616036 | ||||||||
\(146\) | −3.25685e9 | −0.0490946 | ||||||||
\(147\) | 2.88068e9i | 0.0419670i | ||||||||
\(148\) | 2.29195e10i | 0.322772i | ||||||||
\(149\) | 6.05305e10i | 0.824220i | 0.911134 | + | 0.412110i | \(0.135208\pi\) | ||||
−0.911134 | + | 0.412110i | \(0.864792\pi\) | |||||||
\(150\) | 8.08689e8 | 0.0106494 | ||||||||
\(151\) | − | 4.49709e10i | − | 0.572858i | −0.958101 | − | 0.286429i | \(-0.907532\pi\) | ||
0.958101 | − | 0.286429i | \(-0.0924683\pi\) | |||||||
\(152\) | −1.86048e10 | −0.229302 | ||||||||
\(153\) | −2.74401e10 | −0.327286 | ||||||||
\(154\) | −2.87553e9 | −0.0331982 | ||||||||
\(155\) | 1.62796e10i | 0.181964i | ||||||||
\(156\) | 6.98538e10i | 0.756079i | ||||||||
\(157\) | − | 1.13946e11i | − | 1.19454i | −0.802040 | − | 0.597270i | \(-0.796252\pi\) | ||
0.802040 | − | 0.597270i | \(-0.203748\pi\) | |||||||
\(158\) | 2.04260e10i | 0.207443i | ||||||||
\(159\) | − | 5.50182e10i | − | 0.541403i | ||||||
\(160\) | 5.34081e10 | 0.509340 | ||||||||
\(161\) | − | 1.00496e11i | − | 0.929004i | ||||||
\(162\) | − | 2.39965e10i | − | 0.215066i | ||||||
\(163\) | − | 1.77980e11i | − | 1.54680i | −0.633919 | − | 0.773399i | \(-0.718555\pi\) | ||
0.633919 | − | 0.773399i | \(-0.281445\pi\) | |||||||
\(164\) | −7.69968e10 | −0.649013 | ||||||||
\(165\) | 2.96264e10 | 0.242247 | ||||||||
\(166\) | 2.68268e10i | 0.212828i | ||||||||
\(167\) | 1.04020e11 | 0.800820 | 0.400410 | − | 0.916336i | \(-0.368868\pi\) | ||||
0.400410 | + | 0.916336i | \(0.368868\pi\) | |||||||
\(168\) | − | 5.38112e10i | − | 0.402093i | ||||||
\(169\) | −8.02243e10 | −0.581932 | ||||||||
\(170\) | 1.81536e10 | 0.127855 | ||||||||
\(171\) | − | 4.46606e10i | − | 0.305453i | ||||||
\(172\) | 2.88141e10 | + | 1.43194e11i | 0.191409 | + | 0.951223i | ||||
\(173\) | 1.68634e10 | 0.108822 | 0.0544109 | − | 0.998519i | \(-0.482672\pi\) | ||||
0.0544109 | + | 0.998519i | \(0.482672\pi\) | |||||||
\(174\) | − | 1.99062e10i | − | 0.124808i | ||||||
\(175\) | − | 8.26658e9i | − | 0.0503658i | ||||||
\(176\) | 3.01857e10 | 0.178746 | ||||||||
\(177\) | − | 1.67996e11i | − | 0.967012i | ||||||
\(178\) | 3.64884e10 | 0.204200 | ||||||||
\(179\) | 3.41248e10i | 0.185697i | 0.995680 | + | 0.0928484i | \(0.0295972\pi\) | ||||
−0.995680 | + | 0.0928484i | \(0.970403\pi\) | |||||||
\(180\) | 8.50427e10i | 0.450064i | ||||||||
\(181\) | −2.40858e11 | −1.23985 | −0.619924 | − | 0.784662i | \(-0.712836\pi\) | ||||
−0.619924 | + | 0.784662i | \(0.712836\pi\) | |||||||
\(182\) | −2.18642e10 | −0.109491 | ||||||||
\(183\) | −1.42638e10 | −0.0694994 | ||||||||
\(184\) | − | 6.77305e10i | − | 0.321140i | ||||||
\(185\) | 7.39111e10 | 0.341076 | ||||||||
\(186\) | 8.20702e9 | 0.0368656 | ||||||||
\(187\) | 3.24324e10 | 0.141831 | ||||||||
\(188\) | −2.20913e11 | −0.940658 | ||||||||
\(189\) | −1.56359e11 | −0.648357 | ||||||||
\(190\) | 2.95462e10i | 0.119326i | ||||||||
\(191\) | 1.22618e11i | 0.482376i | 0.970478 | + | 0.241188i | \(0.0775370\pi\) | ||||
−0.970478 | + | 0.241188i | \(0.922463\pi\) | |||||||
\(192\) | 2.59774e11i | 0.995610i | ||||||||
\(193\) | 3.39835e10 | 0.126906 | 0.0634530 | − | 0.997985i | \(-0.479789\pi\) | ||||
0.0634530 | + | 0.997985i | \(0.479789\pi\) | |||||||
\(194\) | 2.15796e10i | 0.0785299i | ||||||||
\(195\) | 2.25266e11 | 0.798954 | ||||||||
\(196\) | 9.77345e9 | 0.0337884 | ||||||||
\(197\) | −4.27539e10 | −0.144094 | −0.0720468 | − | 0.997401i | \(-0.522953\pi\) | ||||
−0.0720468 | + | 0.997401i | \(0.522953\pi\) | |||||||
\(198\) | − | 4.65215e9i | − | 0.0152872i | ||||||
\(199\) | 3.23926e11i | 1.03796i | 0.854787 | + | 0.518979i | \(0.173688\pi\) | ||||
−0.854787 | + | 0.518979i | \(0.826312\pi\) | |||||||
\(200\) | − | 5.57138e9i | − | 0.0174106i | ||||||
\(201\) | 1.79109e11i | 0.545931i | ||||||||
\(202\) | 1.67922e10i | 0.0499287i | ||||||||
\(203\) | −2.03486e11 | −0.590274 | ||||||||
\(204\) | 2.98886e11i | 0.845970i | ||||||||
\(205\) | 2.48300e11i | 0.685817i | ||||||||
\(206\) | 9.85250e10i | 0.265589i | ||||||||
\(207\) | 1.62586e11 | 0.427790 | ||||||||
\(208\) | 2.29518e11 | 0.589523 | ||||||||
\(209\) | 5.27860e10i | 0.132369i | ||||||||
\(210\) | −8.54573e10 | −0.209244 | ||||||||
\(211\) | − | 2.63888e11i | − | 0.630967i | −0.948931 | − | 0.315484i | \(-0.897833\pi\) | ||
0.948931 | − | 0.315484i | \(-0.102167\pi\) | |||||||
\(212\) | −1.86664e11 | −0.435894 | ||||||||
\(213\) | 6.34146e11 | 1.44641 | ||||||||
\(214\) | 1.34587e11i | 0.299872i | ||||||||
\(215\) | 4.61774e11 | − | 9.29203e10i | 1.00516 | − | 0.202264i | ||||
\(216\) | −1.05380e11 | −0.224126 | ||||||||
\(217\) | − | 8.38939e10i | − | 0.174354i | ||||||
\(218\) | − | 7.56560e10i | − | 0.153660i | ||||||
\(219\) | −1.72920e11 | −0.343262 | ||||||||
\(220\) | − | 1.00515e11i | − | 0.195038i | ||||||
\(221\) | 2.46602e11 | 0.467772 | ||||||||
\(222\) | − | 3.72608e10i | − | 0.0691015i | ||||||
\(223\) | 5.14534e11i | 0.933018i | 0.884516 | + | 0.466509i | \(0.154488\pi\) | ||||
−0.884516 | + | 0.466509i | \(0.845512\pi\) | |||||||
\(224\) | −2.75229e11 | −0.488039 | ||||||||
\(225\) | 1.33740e10 | 0.0231926 | ||||||||
\(226\) | −3.34756e10 | −0.0567788 | ||||||||
\(227\) | − | 1.64053e11i | − | 0.272179i | −0.990697 | − | 0.136089i | \(-0.956547\pi\) | ||
0.990697 | − | 0.136089i | \(-0.0434534\pi\) | |||||||
\(228\) | −4.86458e11 | −0.789534 | ||||||||
\(229\) | −1.09291e12 | −1.73543 | −0.867716 | − | 0.497060i | \(-0.834413\pi\) | ||||
−0.867716 | + | 0.497060i | \(0.834413\pi\) | |||||||
\(230\) | −1.07562e11 | −0.167117 | ||||||||
\(231\) | −1.52674e11 | −0.232117 | ||||||||
\(232\) | −1.37142e11 | −0.204047 | ||||||||
\(233\) | − | 1.28928e12i | − | 1.87744i | −0.344680 | − | 0.938720i | \(-0.612013\pi\) | ||
0.344680 | − | 0.938720i | \(-0.387987\pi\) | |||||||
\(234\) | − | 3.53728e10i | − | 0.0504186i | ||||||
\(235\) | 7.12403e11i | 0.994000i | ||||||||
\(236\) | −5.69969e11 | −0.778559 | ||||||||
\(237\) | 1.08451e12i | 1.45041i | ||||||||
\(238\) | −9.35513e10 | −0.122508 | ||||||||
\(239\) | 5.08555e11 | 0.652152 | 0.326076 | − | 0.945344i | \(-0.394273\pi\) | ||||
0.326076 | + | 0.945344i | \(0.394273\pi\) | |||||||
\(240\) | 8.97082e11 | 1.12662 | ||||||||
\(241\) | − | 1.38456e12i | − | 1.70304i | −0.524318 | − | 0.851522i | \(-0.675680\pi\) | ||
0.524318 | − | 0.851522i | \(-0.324320\pi\) | |||||||
\(242\) | − | 1.37564e11i | − | 0.165741i | ||||||
\(243\) | − | 7.14909e11i | − | 0.843761i | ||||||
\(244\) | 4.83938e10i | 0.0559552i | ||||||||
\(245\) | − | 3.15176e10i | − | 0.0357044i | ||||||
\(246\) | 1.25176e11 | 0.138946 | ||||||||
\(247\) | 4.01361e11i | 0.436567i | ||||||||
\(248\) | − | 5.65415e10i | − | 0.0602711i | ||||||
\(249\) | 1.42435e12i | 1.48806i | ||||||||
\(250\) | 1.63739e11 | 0.167668 | ||||||||
\(251\) | −4.19781e10 | −0.0421361 | −0.0210680 | − | 0.999778i | \(-0.506707\pi\) | ||||
−0.0210680 | + | 0.999778i | \(0.506707\pi\) | |||||||
\(252\) | − | 4.38253e11i | − | 0.431243i | ||||||
\(253\) | −1.92166e11 | −0.185385 | ||||||||
\(254\) | − | 2.20081e11i | − | 0.208168i | ||||||
\(255\) | 9.63852e11 | 0.893943 | ||||||||
\(256\) | 7.87205e11 | 0.715958 | ||||||||
\(257\) | − | 5.14381e11i | − | 0.458795i | −0.973333 | − | 0.229398i | \(-0.926324\pi\) | ||
0.973333 | − | 0.229398i | \(-0.0736756\pi\) | |||||||
\(258\) | −4.68439e10 | − | 2.32794e11i | −0.0409784 | − | 0.203645i | ||||
\(259\) | −3.80888e11 | −0.326812 | ||||||||
\(260\) | − | 7.64272e11i | − | 0.643252i | ||||||
\(261\) | − | 3.29207e11i | − | 0.271811i | ||||||
\(262\) | 2.38210e11 | 0.192954 | ||||||||
\(263\) | − | 2.20947e12i | − | 1.75594i | −0.478719 | − | 0.877968i | \(-0.658899\pi\) | ||
0.478719 | − | 0.877968i | \(-0.341101\pi\) | |||||||
\(264\) | −1.02897e11 | −0.0802386 | ||||||||
\(265\) | 6.01956e11i | 0.460612i | ||||||||
\(266\) | − | 1.52261e11i | − | 0.114336i | ||||||
\(267\) | 1.93733e12 | 1.42773 | ||||||||
\(268\) | 6.07674e11 | 0.439539 | ||||||||
\(269\) | −5.98549e11 | −0.424950 | −0.212475 | − | 0.977166i | \(-0.568152\pi\) | ||||
−0.212475 | + | 0.977166i | \(0.568152\pi\) | |||||||
\(270\) | 1.67354e11i | 0.116632i | ||||||||
\(271\) | −8.02913e11 | −0.549315 | −0.274658 | − | 0.961542i | \(-0.588565\pi\) | ||||
−0.274658 | + | 0.961542i | \(0.588565\pi\) | |||||||
\(272\) | 9.82048e11 | 0.659612 | ||||||||
\(273\) | −1.16087e12 | −0.765542 | ||||||||
\(274\) | 4.29386e10 | 0.0278032 | ||||||||
\(275\) | −1.58072e10 | −0.0100506 | ||||||||
\(276\) | − | 1.77094e12i | − | 1.10575i | ||||||
\(277\) | − | 3.55023e11i | − | 0.217700i | −0.994058 | − | 0.108850i | \(-0.965283\pi\) | ||
0.994058 | − | 0.108850i | \(-0.0347168\pi\) | |||||||
\(278\) | 4.21444e11i | 0.253814i | ||||||||
\(279\) | 1.35727e11 | 0.0802869 | ||||||||
\(280\) | 5.88750e11i | 0.342090i | ||||||||
\(281\) | 9.07881e11 | 0.518200 | 0.259100 | − | 0.965851i | \(-0.416574\pi\) | ||||
0.259100 | + | 0.965851i | \(0.416574\pi\) | |||||||
\(282\) | 3.59144e11 | 0.201383 | ||||||||
\(283\) | −1.06931e12 | −0.589074 | −0.294537 | − | 0.955640i | \(-0.595165\pi\) | ||||
−0.294537 | + | 0.955640i | \(0.595165\pi\) | |||||||
\(284\) | − | 2.15150e12i | − | 1.16453i | ||||||
\(285\) | 1.56874e12i | 0.834307i | ||||||||
\(286\) | 4.18085e10i | 0.0218491i | ||||||||
\(287\) | − | 1.27957e12i | − | 0.657136i | ||||||
\(288\) | − | 4.45277e11i | − | 0.224733i | ||||||
\(289\) | −9.60851e11 | −0.476614 | ||||||||
\(290\) | 2.17795e11i | 0.106183i | ||||||||
\(291\) | 1.14575e12i | 0.549069i | ||||||||
\(292\) | 5.86677e11i | 0.276366i | ||||||||
\(293\) | −3.17887e12 | −1.47209 | −0.736046 | − | 0.676932i | \(-0.763309\pi\) | ||||
−0.736046 | + | 0.676932i | \(0.763309\pi\) | |||||||
\(294\) | −1.58890e10 | −0.00723367 | ||||||||
\(295\) | 1.83805e12i | 0.822709i | ||||||||
\(296\) | −2.56705e11 | −0.112973 | ||||||||
\(297\) | 2.98988e11i | 0.129381i | ||||||||
\(298\) | −3.33868e11 | −0.142067 | ||||||||
\(299\) | −1.46115e12 | −0.611417 | ||||||||
\(300\) | − | 1.45674e11i | − | 0.0599482i | ||||||
\(301\) | −2.37967e12 | + | 4.78848e11i | −0.963129 | + | 0.193805i | ||||
\(302\) | 2.48046e11 | 0.0987411 | ||||||||
\(303\) | 8.91569e11i | 0.349093i | ||||||||
\(304\) | 1.59835e12i | 0.615608i | ||||||||
\(305\) | 1.56061e11 | 0.0591283 | ||||||||
\(306\) | − | 1.51351e11i | − | 0.0564129i | ||||||
\(307\) | −1.42283e11 | −0.0521749 | −0.0260875 | − | 0.999660i | \(-0.508305\pi\) | ||||
−0.0260875 | + | 0.999660i | \(0.508305\pi\) | |||||||
\(308\) | 5.17987e11i | 0.186881i | ||||||||
\(309\) | 5.23112e12i | 1.85696i | ||||||||
\(310\) | −8.97932e10 | −0.0313643 | ||||||||
\(311\) | 2.92237e12 | 1.00446 | 0.502231 | − | 0.864733i | \(-0.332513\pi\) | ||||
0.502231 | + | 0.864733i | \(0.332513\pi\) | |||||||
\(312\) | −7.82383e11 | −0.264634 | ||||||||
\(313\) | − | 3.24566e11i | − | 0.108039i | −0.998540 | − | 0.0540195i | \(-0.982797\pi\) | ||
0.998540 | − | 0.0540195i | \(-0.0172033\pi\) | |||||||
\(314\) | 6.28492e11 | 0.205898 | ||||||||
\(315\) | −1.41328e12 | −0.455697 | ||||||||
\(316\) | 3.67947e12 | 1.16775 | ||||||||
\(317\) | 5.95423e12 | 1.86007 | 0.930034 | − | 0.367473i | \(-0.119777\pi\) | ||||
0.930034 | + | 0.367473i | \(0.119777\pi\) | |||||||
\(318\) | 3.03464e11 | 0.0933193 | ||||||||
\(319\) | 3.89102e11i | 0.117791i | ||||||||
\(320\) | − | 2.84219e12i | − | 0.847039i | ||||||
\(321\) | 7.14582e12i | 2.09666i | ||||||||
\(322\) | 5.54304e11 | 0.160128 | ||||||||
\(323\) | 1.71732e12i | 0.488470i | ||||||||
\(324\) | −4.32263e12 | −1.21066 | ||||||||
\(325\) | −1.20191e11 | −0.0331479 | ||||||||
\(326\) | 9.81685e11 | 0.266615 | ||||||||
\(327\) | − | 4.01690e12i | − | 1.07437i | ||||||
\(328\) | − | 8.62386e11i | − | 0.227160i | ||||||
\(329\) | − | 3.67124e12i | − | 0.952431i | ||||||
\(330\) | 1.63410e11i | 0.0417551i | ||||||||
\(331\) | 4.61496e12i | 1.16152i | 0.814073 | + | 0.580762i | \(0.197245\pi\) | ||||
−0.814073 | + | 0.580762i | \(0.802755\pi\) | |||||||
\(332\) | 4.83248e12 | 1.19806 | ||||||||
\(333\) | − | 6.16216e11i | − | 0.150491i | ||||||
\(334\) | 5.73743e11i | 0.138034i | ||||||||
\(335\) | − | 1.95964e12i | − | 0.464464i | ||||||
\(336\) | −4.62295e12 | −1.07950 | ||||||||
\(337\) | 5.38665e12 | 1.23928 | 0.619640 | − | 0.784886i | \(-0.287279\pi\) | ||||
0.619640 | + | 0.784886i | \(0.287279\pi\) | |||||||
\(338\) | − | 4.42493e11i | − | 0.100305i | ||||||
\(339\) | −1.77737e12 | −0.396989 | ||||||||
\(340\) | − | 3.27012e12i | − | 0.719729i | ||||||
\(341\) | −1.60421e11 | −0.0347927 | ||||||||
\(342\) | 2.46334e11 | 0.0526495 | ||||||||
\(343\) | 4.82659e12i | 1.01665i | ||||||||
\(344\) | −1.60381e12 | + | 3.22727e11i | −0.332937 | + | 0.0669950i | ||||
\(345\) | −5.71095e12 | −1.16846 | ||||||||
\(346\) | 9.30137e10i | 0.0187571i | ||||||||
\(347\) | 8.09633e12i | 1.60931i | 0.593740 | + | 0.804657i | \(0.297651\pi\) | ||||
−0.593740 | + | 0.804657i | \(0.702349\pi\) | |||||||
\(348\) | −3.58583e12 | −0.702577 | ||||||||
\(349\) | − | 5.38376e12i | − | 1.03982i | −0.854221 | − | 0.519910i | \(-0.825965\pi\) | ||
0.854221 | − | 0.519910i | \(-0.174035\pi\) | |||||||
\(350\) | 4.55960e10 | 0.00868133 | ||||||||
\(351\) | 2.27337e12i | 0.426711i | ||||||||
\(352\) | 5.26289e11i | 0.0973893i | ||||||||
\(353\) | 4.06273e12 | 0.741215 | 0.370608 | − | 0.928790i | \(-0.379149\pi\) | ||||
0.370608 | + | 0.928790i | \(0.379149\pi\) | |||||||
\(354\) | 9.26614e11 | 0.166680 | ||||||||
\(355\) | −6.93820e12 | −1.23057 | ||||||||
\(356\) | − | 6.57288e12i | − | 1.14949i | ||||||
\(357\) | −4.96704e12 | −0.856558 | ||||||||
\(358\) | −1.88222e11 | −0.0320078 | ||||||||
\(359\) | −7.21622e12 | −1.21015 | −0.605073 | − | 0.796170i | \(-0.706856\pi\) | ||||
−0.605073 | + | 0.796170i | \(0.706856\pi\) | |||||||
\(360\) | −9.52503e11 | −0.157527 | ||||||||
\(361\) | 3.33601e12 | 0.544116 | ||||||||
\(362\) | − | 1.32850e12i | − | 0.213707i | ||||||
\(363\) | − | 7.30389e12i | − | 1.15883i | ||||||
\(364\) | 3.93854e12i | 0.616351i | ||||||||
\(365\) | 1.89192e12 | 0.292038 | ||||||||
\(366\) | − | 7.86750e10i | − | 0.0119793i | ||||||
\(367\) | 1.20158e13 | 1.80477 | 0.902385 | − | 0.430931i | \(-0.141815\pi\) | ||||
0.902385 | + | 0.430931i | \(0.141815\pi\) | |||||||
\(368\) | −5.81876e12 | −0.862167 | ||||||||
\(369\) | 2.07014e12 | 0.302600 | ||||||||
\(370\) | 4.07672e11i | 0.0587898i | ||||||||
\(371\) | − | 3.10207e12i | − | 0.441349i | ||||||
\(372\) | − | 1.47838e12i | − | 0.207526i | ||||||
\(373\) | 5.46051e12i | 0.756291i | 0.925746 | + | 0.378146i | \(0.123438\pi\) | ||||
−0.925746 | + | 0.378146i | \(0.876562\pi\) | |||||||
\(374\) | 1.78887e11i | 0.0244468i | ||||||||
\(375\) | 8.69359e12 | 1.17231 | ||||||||
\(376\) | − | 2.47429e12i | − | 0.329239i | ||||||
\(377\) | 2.95856e12i | 0.388484i | ||||||||
\(378\) | − | 8.62429e11i | − | 0.111754i | ||||||
\(379\) | 2.08400e12 | 0.266503 | 0.133251 | − | 0.991082i | \(-0.457458\pi\) | ||||
0.133251 | + | 0.991082i | \(0.457458\pi\) | |||||||
\(380\) | 5.32235e12 | 0.671715 | ||||||||
\(381\) | − | 1.16850e13i | − | 1.45547i | ||||||
\(382\) | −6.76321e11 | −0.0831450 | ||||||||
\(383\) | − | 6.42552e12i | − | 0.779676i | −0.920883 | − | 0.389838i | \(-0.872531\pi\) | ||
0.920883 | − | 0.389838i | \(-0.127469\pi\) | |||||||
\(384\) | −6.43145e12 | −0.770287 | ||||||||
\(385\) | 1.67041e12 | 0.197479 | ||||||||
\(386\) | 1.87443e11i | 0.0218742i | ||||||||
\(387\) | −7.74700e11 | − | 3.84993e12i | −0.0892439 | − | 0.443504i | ||||
\(388\) | 3.88727e12 | 0.442065 | ||||||||
\(389\) | − | 6.24207e12i | − | 0.700779i | −0.936604 | − | 0.350389i | \(-0.886049\pi\) | ||
0.936604 | − | 0.350389i | \(-0.113951\pi\) | |||||||
\(390\) | 1.24250e12i | 0.137712i | ||||||||
\(391\) | −6.25186e12 | −0.684109 | ||||||||
\(392\) | 1.09465e11i | 0.0118262i | ||||||||
\(393\) | 1.26476e13 | 1.34910 | ||||||||
\(394\) | − | 2.35818e11i | − | 0.0248368i | ||||||
\(395\) | − | 1.18656e13i | − | 1.23397i | ||||||
\(396\) | −8.38020e11 | −0.0860555 | ||||||||
\(397\) | −3.04685e12 | −0.308958 | −0.154479 | − | 0.987996i | \(-0.549370\pi\) | ||||
−0.154479 | + | 0.987996i | \(0.549370\pi\) | |||||||
\(398\) | −1.78668e12 | −0.178908 | ||||||||
\(399\) | − | 8.08421e12i | − | 0.799416i | ||||||
\(400\) | −4.78641e11 | −0.0467422 | ||||||||
\(401\) | −5.06144e12 | −0.488149 | −0.244074 | − | 0.969757i | \(-0.578484\pi\) | ||||
−0.244074 | + | 0.969757i | \(0.578484\pi\) | |||||||
\(402\) | −9.87912e11 | −0.0940997 | ||||||||
\(403\) | −1.21977e12 | −0.114750 | ||||||||
\(404\) | 3.02488e12 | 0.281061 | ||||||||
\(405\) | 1.39397e13i | 1.27932i | ||||||||
\(406\) | − | 1.12237e12i | − | 0.101743i | ||||||
\(407\) | 7.28328e11i | 0.0652161i | ||||||||
\(408\) | −3.34761e12 | −0.296097 | ||||||||
\(409\) | 9.21342e12i | 0.805016i | 0.915416 | + | 0.402508i | \(0.131861\pi\) | ||||
−0.915416 | + | 0.402508i | \(0.868139\pi\) | |||||||
\(410\) | −1.36955e12 | −0.118211 | ||||||||
\(411\) | 2.27979e12 | 0.194396 | ||||||||
\(412\) | 1.77479e13 | 1.49507 | ||||||||
\(413\) | − | 9.47204e12i | − | 0.788303i | ||||||
\(414\) | 8.96774e11i | 0.0737363i | ||||||||
\(415\) | − | 1.55839e13i | − | 1.26600i | ||||||
\(416\) | 4.00167e12i | 0.321199i | ||||||||
\(417\) | 2.23763e13i | 1.77463i | ||||||||
\(418\) | −2.91152e11 | −0.0228159 | ||||||||
\(419\) | − | 1.86619e13i | − | 1.44506i | −0.691339 | − | 0.722531i | \(-0.742979\pi\) | ||
0.691339 | − | 0.722531i | \(-0.257021\pi\) | |||||||
\(420\) | 1.53940e13i | 1.17789i | ||||||||
\(421\) | 8.57888e12i | 0.648665i | 0.945943 | + | 0.324332i | \(0.105140\pi\) | ||||
−0.945943 | + | 0.324332i | \(0.894860\pi\) | |||||||
\(422\) | 1.45552e12 | 0.108757 | ||||||||
\(423\) | 5.93948e12 | 0.438578 | ||||||||
\(424\) | − | 2.09069e12i | − | 0.152567i | ||||||
\(425\) | −5.14266e11 | −0.0370889 | ||||||||
\(426\) | 3.49776e12i | 0.249311i | ||||||||
\(427\) | −8.04232e11 | −0.0566555 | ||||||||
\(428\) | 2.42441e13 | 1.68805 | ||||||||
\(429\) | 2.21979e12i | 0.152766i | ||||||||
\(430\) | 5.12520e11 | + | 2.54701e12i | 0.0348633 | + | 0.173256i | ||||
\(431\) | −2.69197e13 | −1.81002 | −0.905010 | − | 0.425390i | \(-0.860137\pi\) | ||||
−0.905010 | + | 0.425390i | \(0.860137\pi\) | |||||||
\(432\) | 9.05329e12i | 0.601711i | ||||||||
\(433\) | 1.86409e13i | 1.22469i | 0.790590 | + | 0.612346i | \(0.209774\pi\) | ||||
−0.790590 | + | 0.612346i | \(0.790226\pi\) | |||||||
\(434\) | 4.62733e11 | 0.0300526 | ||||||||
\(435\) | 1.15636e13i | 0.742418i | ||||||||
\(436\) | −1.36284e13 | −0.864992 | ||||||||
\(437\) | − | 1.01753e13i | − | 0.638471i | ||||||
\(438\) | − | 9.53776e11i | − | 0.0591665i | ||||||
\(439\) | −1.34913e13 | −0.827428 | −0.413714 | − | 0.910407i | \(-0.635769\pi\) | ||||
−0.413714 | + | 0.910407i | \(0.635769\pi\) | |||||||
\(440\) | 1.12580e12 | 0.0682649 | ||||||||
\(441\) | −2.62770e11 | −0.0157537 | ||||||||
\(442\) | 1.36018e12i | 0.0806278i | ||||||||
\(443\) | −1.26659e13 | −0.742367 | −0.371184 | − | 0.928559i | \(-0.621048\pi\) | ||||
−0.371184 | + | 0.928559i | \(0.621048\pi\) | |||||||
\(444\) | −6.71202e12 | −0.388990 | ||||||||
\(445\) | −2.11963e13 | −1.21468 | ||||||||
\(446\) | −2.83802e12 | −0.160820 | ||||||||
\(447\) | −1.77265e13 | −0.993311 | ||||||||
\(448\) | 1.46467e13i | 0.811616i | ||||||||
\(449\) | − | 2.11844e13i | − | 1.16087i | −0.814306 | − | 0.580436i | \(-0.802882\pi\) | ||
0.814306 | − | 0.580436i | \(-0.197118\pi\) | |||||||
\(450\) | 7.37670e10i | 0.00399760i | ||||||||
\(451\) | −2.44678e12 | −0.131133 | ||||||||
\(452\) | 6.03017e12i | 0.319623i | ||||||||
\(453\) | 1.31698e13 | 0.690382 | ||||||||
\(454\) | 9.04866e11 | 0.0469143 | ||||||||
\(455\) | 1.27011e13 | 0.651303 | ||||||||
\(456\) | − | 5.44847e12i | − | 0.276344i | ||||||
\(457\) | − | 1.61516e13i | − | 0.810277i | −0.914255 | − | 0.405138i | \(-0.867223\pi\) | ||
0.914255 | − | 0.405138i | \(-0.132777\pi\) | |||||||
\(458\) | − | 6.02817e12i | − | 0.299129i | ||||||
\(459\) | 9.72714e12i | 0.477443i | ||||||||
\(460\) | 1.93759e13i | 0.940746i | ||||||||
\(461\) | 4.88602e11 | 0.0234666 | 0.0117333 | − | 0.999931i | \(-0.496265\pi\) | ||||
0.0117333 | + | 0.999931i | \(0.496265\pi\) | |||||||
\(462\) | − | 8.42105e11i | − | 0.0400089i | ||||||
\(463\) | 2.11110e13i | 0.992210i | 0.868263 | + | 0.496105i | \(0.165237\pi\) | ||||
−0.868263 | + | 0.496105i | \(0.834763\pi\) | |||||||
\(464\) | 1.17819e13i | 0.547807i | ||||||||
\(465\) | −4.76751e12 | −0.219294 | ||||||||
\(466\) | 7.11126e12 | 0.323606 | ||||||||
\(467\) | − | 2.80571e13i | − | 1.26316i | −0.775311 | − | 0.631580i | \(-0.782407\pi\) | ||
0.775311 | − | 0.631580i | \(-0.217593\pi\) | |||||||
\(468\) | −6.37193e12 | −0.283819 | ||||||||
\(469\) | 1.00986e13i | 0.445040i | ||||||||
\(470\) | −3.92940e12 | −0.171331 | ||||||||
\(471\) | 3.33693e13 | 1.43960 | ||||||||
\(472\) | − | 6.38382e12i | − | 0.272503i | ||||||
\(473\) | 9.15647e11 | + | 4.55037e12i | 0.0386743 | + | 0.192195i | ||||
\(474\) | −5.98181e12 | −0.250001 | ||||||||
\(475\) | − | 8.37004e11i | − | 0.0346146i | ||||||
\(476\) | 1.68520e13i | 0.689630i | ||||||||
\(477\) | 5.01866e12 | 0.203234 | ||||||||
\(478\) | 2.80504e12i | 0.112409i | ||||||||
\(479\) | 2.61293e13 | 1.03622 | 0.518108 | − | 0.855315i | \(-0.326636\pi\) | ||||
0.518108 | + | 0.855315i | \(0.326636\pi\) | |||||||
\(480\) | 1.56407e13i | 0.613832i | ||||||||
\(481\) | 5.53788e12i | 0.215089i | ||||||||
\(482\) | 7.63681e12 | 0.293546 | ||||||||
\(483\) | 2.94304e13 | 1.11959 | ||||||||
\(484\) | −2.47803e13 | −0.932998 | ||||||||
\(485\) | − | 1.25357e13i | − | 0.467133i | ||||||
\(486\) | 3.94322e12 | 0.145435 | ||||||||
\(487\) | −2.80825e13 | −1.02516 | −0.512579 | − | 0.858640i | \(-0.671310\pi\) | ||||
−0.512579 | + | 0.858640i | \(0.671310\pi\) | |||||||
\(488\) | −5.42024e11 | −0.0195848 | ||||||||
\(489\) | 5.21219e13 | 1.86413 | ||||||||
\(490\) | 1.73841e11 | 0.00615422 | ||||||||
\(491\) | 2.65400e13i | 0.930024i | 0.885304 | + | 0.465012i | \(0.153950\pi\) | ||||
−0.885304 | + | 0.465012i | \(0.846050\pi\) | |||||||
\(492\) | − | 2.25487e13i | − | 0.782160i | ||||||
\(493\) | 1.26589e13i | 0.434671i | ||||||||
\(494\) | −2.21379e12 | −0.0752491 | ||||||||
\(495\) | 2.70246e12i | 0.0909355i | ||||||||
\(496\) | −4.85751e12 | −0.161810 | ||||||||
\(497\) | 3.57548e13 | 1.17910 | ||||||||
\(498\) | −7.85630e12 | −0.256490 | ||||||||
\(499\) | − | 5.01516e13i | − | 1.62100i | −0.585741 | − | 0.810499i | \(-0.699196\pi\) | ||
0.585741 | − | 0.810499i | \(-0.300804\pi\) | |||||||
\(500\) | − | 2.94953e13i | − | 0.943848i | ||||||
\(501\) | 3.04625e13i | 0.965110i | ||||||||
\(502\) | − | 2.31538e11i | − | 0.00726281i | ||||||
\(503\) | 4.15535e13i | 1.29053i | 0.763959 | + | 0.645264i | \(0.223253\pi\) | ||||
−0.763959 | + | 0.645264i | \(0.776747\pi\) | |||||||
\(504\) | 4.90855e12 | 0.150939 | ||||||||
\(505\) | − | 9.75467e12i | − | 0.297000i | ||||||
\(506\) | − | 1.05993e12i | − | 0.0319540i | ||||||
\(507\) | − | 2.34939e13i | − | 0.701318i | ||||||
\(508\) | −3.96445e13 | −1.17183 | ||||||||
\(509\) | −1.85803e13 | −0.543831 | −0.271916 | − | 0.962321i | \(-0.587657\pi\) | ||||
−0.271916 | + | 0.962321i | \(0.587657\pi\) | |||||||
\(510\) | 5.31632e12i | 0.154085i | ||||||||
\(511\) | −9.74970e12 | −0.279825 | ||||||||
\(512\) | 2.68305e13i | 0.762568i | ||||||||
\(513\) | −1.58316e13 | −0.445592 | ||||||||
\(514\) | 2.83717e12 | 0.0790805 | ||||||||
\(515\) | − | 5.72338e13i | − | 1.57985i | ||||||
\(516\) | −4.19347e13 | + | 8.43828e12i | −1.14637 | + | 0.230678i | ||||
\(517\) | −7.02010e12 | −0.190060 | ||||||||
\(518\) | − | 2.10086e12i | − | 0.0563312i | ||||||
\(519\) | 4.93850e12i | 0.131147i | ||||||||
\(520\) | 8.56007e12 | 0.225144 | ||||||||
\(521\) | − | 4.29356e13i | − | 1.11848i | −0.829005 | − | 0.559241i | \(-0.811093\pi\) | ||
0.829005 | − | 0.559241i | \(-0.188907\pi\) | |||||||
\(522\) | 1.81581e12 | 0.0468508 | ||||||||
\(523\) | − | 5.43272e13i | − | 1.38838i | −0.719791 | − | 0.694191i | \(-0.755762\pi\) | ||
0.719791 | − | 0.694191i | \(-0.244238\pi\) | |||||||
\(524\) | − | 4.29102e13i | − | 1.08619i | ||||||
\(525\) | 2.42089e12 | 0.0606985 | ||||||||
\(526\) | 1.21868e13 | 0.302663 | ||||||||
\(527\) | −5.21906e12 | −0.128392 | ||||||||
\(528\) | 8.83994e12i | 0.215417i | ||||||||
\(529\) | −4.38346e12 | −0.105813 | ||||||||
\(530\) | −3.32021e12 | −0.0793937 | ||||||||
\(531\) | 1.53242e13 | 0.363000 | ||||||||
\(532\) | −2.74278e13 | −0.643624 | ||||||||
\(533\) | −1.86042e13 | −0.432489 | ||||||||
\(534\) | 1.06857e13i | 0.246092i | ||||||||
\(535\) | − | 7.81826e13i | − | 1.78378i | ||||||
\(536\) | 6.80613e12i | 0.153842i | ||||||||
\(537\) | −9.99351e12 | −0.223793 | ||||||||
\(538\) | − | 3.30141e12i | − | 0.0732468i | ||||||
\(539\) | 3.10577e11 | 0.00682694 | ||||||||
\(540\) | 3.01465e13 | 0.656551 | ||||||||
\(541\) | 2.25829e13 | 0.487297 | 0.243648 | − | 0.969864i | \(-0.421656\pi\) | ||||
0.243648 | + | 0.969864i | \(0.421656\pi\) | |||||||
\(542\) | − | 4.42862e12i | − | 0.0946831i | ||||||
\(543\) | − | 7.05358e13i | − | 1.49421i | ||||||
\(544\) | 1.71221e13i | 0.359387i | ||||||||
\(545\) | 4.39490e13i | 0.914043i | ||||||||
\(546\) | − | 6.40299e12i | − | 0.131953i | ||||||
\(547\) | 3.55882e13 | 0.726724 | 0.363362 | − | 0.931648i | \(-0.381629\pi\) | ||||
0.363362 | + | 0.931648i | \(0.381629\pi\) | |||||||
\(548\) | − | 7.73479e12i | − | 0.156511i | ||||||
\(549\) | − | 1.30112e12i | − | 0.0260889i | ||||||
\(550\) | − | 8.71880e10i | − | 0.00173238i | ||||||
\(551\) | −2.06032e13 | −0.405674 | ||||||||
\(552\) | 1.98350e13 | 0.387023 | ||||||||
\(553\) | 6.11473e13i | 1.18237i | ||||||||
\(554\) | 1.95820e12 | 0.0375240 | ||||||||
\(555\) | 2.16450e13i | 0.411049i | ||||||||
\(556\) | 7.59173e13 | 1.42878 | ||||||||
\(557\) | −8.95325e13 | −1.66995 | −0.834977 | − | 0.550285i | \(-0.814519\pi\) | ||||
−0.834977 | + | 0.550285i | \(0.814519\pi\) | |||||||
\(558\) | 7.48629e11i | 0.0138387i | ||||||||
\(559\) | 6.96216e12 | + | 3.45990e13i | 0.127551 | + | 0.633876i | ||||
\(560\) | 5.05798e13 | 0.918411 | ||||||||
\(561\) | 9.49791e12i | 0.170928i | ||||||||
\(562\) | 5.00760e12i | 0.0893198i | ||||||||
\(563\) | −3.15967e13 | −0.558598 | −0.279299 | − | 0.960204i | \(-0.590102\pi\) | ||||
−0.279299 | + | 0.960204i | \(0.590102\pi\) | |||||||
\(564\) | − | 6.46948e13i | − | 1.13364i | ||||||
\(565\) | 1.94462e13 | 0.337748 | ||||||||
\(566\) | − | 5.89797e12i | − | 0.101536i | ||||||
\(567\) | − | 7.18358e13i | − | 1.22582i | ||||||
\(568\) | 2.40975e13 | 0.407596 | ||||||||
\(569\) | 5.74761e13 | 0.963665 | 0.481832 | − | 0.876263i | \(-0.339971\pi\) | ||||
0.481832 | + | 0.876263i | \(0.339971\pi\) | |||||||
\(570\) | −8.65268e12 | −0.143806 | ||||||||
\(571\) | 4.22519e13i | 0.696090i | 0.937478 | + | 0.348045i | \(0.113154\pi\) | ||||
−0.937478 | + | 0.348045i | \(0.886846\pi\) | |||||||
\(572\) | 7.53122e12 | 0.122994 | ||||||||
\(573\) | −3.59088e13 | −0.581337 | ||||||||
\(574\) | 7.05774e12 | 0.113268 | ||||||||
\(575\) | 3.04709e12 | 0.0484782 | ||||||||
\(576\) | −2.36961e13 | −0.373735 | ||||||||
\(577\) | 8.04729e13i | 1.25826i | 0.777300 | + | 0.629131i | \(0.216589\pi\) | ||||
−0.777300 | + | 0.629131i | \(0.783411\pi\) | |||||||
\(578\) | − | 5.29976e12i | − | 0.0821518i | ||||||
\(579\) | 9.95215e12i | 0.152941i | ||||||||
\(580\) | 3.92327e13 | 0.597734 | ||||||||
\(581\) | 8.03087e13i | 1.21306i | ||||||||
\(582\) | −6.31964e12 | −0.0946405 | ||||||||
\(583\) | −5.93174e12 | −0.0880723 | ||||||||
\(584\) | −6.57095e12 | −0.0967306 | ||||||||
\(585\) | 2.05483e13i | 0.299914i | ||||||||
\(586\) | − | 1.75337e13i | − | 0.253738i | ||||||
\(587\) | 1.08267e14i | 1.55348i | 0.629822 | + | 0.776739i | \(0.283128\pi\) | ||||
−0.629822 | + | 0.776739i | \(0.716872\pi\) | |||||||
\(588\) | 2.86218e12i | 0.0407202i | ||||||||
\(589\) | − | 8.49438e12i | − | 0.119827i | ||||||
\(590\) | −1.01381e13 | −0.141807 | ||||||||
\(591\) | − | 1.25206e13i | − | 0.173655i | ||||||
\(592\) | 2.20537e13i | 0.303300i | ||||||||
\(593\) | 1.10196e14i | 1.50278i | 0.659861 | + | 0.751388i | \(0.270615\pi\) | ||||
−0.659861 | + | 0.751388i | \(0.729385\pi\) | |||||||
\(594\) | −1.64913e12 | −0.0223009 | ||||||||
\(595\) | 5.43445e13 | 0.728737 | ||||||||
\(596\) | 6.01417e13i | 0.799732i | ||||||||
\(597\) | −9.48623e13 | −1.25090 | ||||||||
\(598\) | − | 8.05924e12i | − | 0.105387i | ||||||
\(599\) | −2.01917e13 | −0.261841 | −0.130921 | − | 0.991393i | \(-0.541793\pi\) | ||||
−0.130921 | + | 0.991393i | \(0.541793\pi\) | |||||||
\(600\) | 1.63159e12 | 0.0209824 | ||||||||
\(601\) | − | 6.69262e13i | − | 0.853539i | −0.904360 | − | 0.426770i | \(-0.859652\pi\) | ||
0.904360 | − | 0.426770i | \(-0.140348\pi\) | |||||||
\(602\) | −2.64118e12 | − | 1.31255e13i | −0.0334053 | − | 0.166010i | ||||
\(603\) | −1.63380e13 | −0.204933 | ||||||||
\(604\) | − | 4.46821e13i | − | 0.555839i | ||||||
\(605\) | 7.99120e13i | 0.985905i | ||||||||
\(606\) | −4.91762e12 | −0.0601717 | ||||||||
\(607\) | − | 1.38942e14i | − | 1.68613i | −0.537815 | − | 0.843063i | \(-0.680750\pi\) | ||
0.537815 | − | 0.843063i | \(-0.319250\pi\) | |||||||
\(608\) | −2.78674e13 | −0.335412 | ||||||||
\(609\) | − | 5.95912e13i | − | 0.711370i | ||||||
\(610\) | 8.60785e11i | 0.0101917i | ||||||||
\(611\) | −5.33776e13 | −0.626835 | ||||||||
\(612\) | −2.72638e13 | −0.317563 | ||||||||
\(613\) | −5.52303e13 | −0.638080 | −0.319040 | − | 0.947741i | \(-0.603360\pi\) | ||||
−0.319040 | + | 0.947741i | \(0.603360\pi\) | |||||||
\(614\) | − | 7.84791e11i | − | 0.00899316i | ||||||
\(615\) | −7.27153e13 | −0.826514 | ||||||||
\(616\) | −5.80160e12 | −0.0654101 | ||||||||
\(617\) | −6.03257e13 | −0.674647 | −0.337324 | − | 0.941389i | \(-0.609522\pi\) | ||||
−0.337324 | + | 0.941389i | \(0.609522\pi\) | |||||||
\(618\) | −2.88533e13 | −0.320076 | ||||||||
\(619\) | 1.44434e14 | 1.58934 | 0.794671 | − | 0.607041i | \(-0.207644\pi\) | ||||
0.794671 | + | 0.607041i | \(0.207644\pi\) | |||||||
\(620\) | 1.61750e13i | 0.176557i | ||||||||
\(621\) | − | 5.76345e13i | − | 0.624058i | ||||||
\(622\) | 1.61189e13i | 0.173135i | ||||||||
\(623\) | 1.09232e14 | 1.16388 | ||||||||
\(624\) | 6.72149e13i | 0.710465i | ||||||||
\(625\) | −1.00006e14 | −1.04864 | ||||||||
\(626\) | 1.79021e12 | 0.0186222 | ||||||||
\(627\) | −1.54585e13 | −0.159525 | ||||||||
\(628\) | − | 1.13214e14i | − | 1.15905i | ||||||
\(629\) | 2.36951e13i | 0.240661i | ||||||||
\(630\) | − | 7.79525e12i | − | 0.0785466i | ||||||
\(631\) | 1.75437e14i | 1.75378i | 0.480692 | + | 0.876890i | \(0.340386\pi\) | ||||
−0.480692 | + | 0.876890i | \(0.659614\pi\) | |||||||
\(632\) | 4.12111e13i | 0.408723i | ||||||||
\(633\) | 7.72801e13 | 0.760412 | ||||||||
\(634\) | 3.28417e13i | 0.320612i | ||||||||
\(635\) | 1.27846e14i | 1.23828i | ||||||||
\(636\) | − | 5.46649e13i | − | 0.525318i | ||||||
\(637\) | 2.36149e12 | 0.0225159 | ||||||||
\(638\) | −2.14617e12 | −0.0203030 | ||||||||
\(639\) | 5.78455e13i | 0.542957i | ||||||||
\(640\) | 7.03666e13 | 0.655340 | ||||||||
\(641\) | 1.42208e14i | 1.31412i | 0.753838 | + | 0.657060i | \(0.228200\pi\) | ||||
−0.753838 | + | 0.657060i | \(0.771800\pi\) | |||||||
\(642\) | −3.94142e13 | −0.361391 | ||||||||
\(643\) | 1.12154e14 | 1.02037 | 0.510186 | − | 0.860064i | \(-0.329577\pi\) | ||||
0.510186 | + | 0.860064i | \(0.329577\pi\) | |||||||
\(644\) | − | 9.98501e13i | − | 0.901404i | ||||||
\(645\) | 2.72119e13 | + | 1.35232e14i | 0.243759 | + | 1.21138i | ||||
\(646\) | −9.47221e12 | −0.0841955 | ||||||||
\(647\) | − | 9.56448e13i | − | 0.843607i | −0.906687 | − | 0.421803i | \(-0.861397\pi\) | ||
0.906687 | − | 0.421803i | \(-0.138603\pi\) | |||||||
\(648\) | − | 4.84147e13i | − | 0.423743i | ||||||
\(649\) | −1.81123e13 | −0.157308 | ||||||||
\(650\) | − | 6.62938e11i | − | 0.00571355i | ||||||
\(651\) | 2.45685e13 | 0.210123 | ||||||||
\(652\) | − | 1.76837e14i | − | 1.50084i | ||||||
\(653\) | − | 7.62193e13i | − | 0.641947i | −0.947088 | − | 0.320974i | \(-0.895990\pi\) | ||
0.947088 | − | 0.320974i | \(-0.104010\pi\) | |||||||
\(654\) | 2.21560e13 | 0.185184 | ||||||||
\(655\) | −1.38377e14 | −1.14778 | ||||||||
\(656\) | −7.40881e13 | −0.609858 | ||||||||
\(657\) | − | 1.57735e13i | − | 0.128855i | ||||||
\(658\) | 2.02495e13 | 0.164166 | ||||||||
\(659\) | 1.91006e14 | 1.53681 | 0.768403 | − | 0.639967i | \(-0.221052\pi\) | ||||
0.768403 | + | 0.639967i | \(0.221052\pi\) | |||||||
\(660\) | 2.94361e13 | 0.235050 | ||||||||
\(661\) | −1.55645e13 | −0.123347 | −0.0616733 | − | 0.998096i | \(-0.519644\pi\) | ||||
−0.0616733 | + | 0.998096i | \(0.519644\pi\) | |||||||
\(662\) | −2.54548e13 | −0.200207 | ||||||||
\(663\) | 7.22178e13i | 0.563737i | ||||||||
\(664\) | 5.41252e13i | 0.419333i | ||||||||
\(665\) | 8.84495e13i | 0.680122i | ||||||||
\(666\) | 3.39886e12 | 0.0259395 | ||||||||
\(667\) | − | 7.50055e13i | − | 0.568152i | ||||||
\(668\) | 1.03352e14 | 0.777027 | ||||||||
\(669\) | −1.50682e14 | −1.12443 | ||||||||
\(670\) | 1.08088e13 | 0.0800576 | ||||||||
\(671\) | 1.53784e12i | 0.0113057i | ||||||||
\(672\) | − | 8.06015e13i | − | 0.588162i | ||||||
\(673\) | − | 5.98762e13i | − | 0.433690i | −0.976206 | − | 0.216845i | \(-0.930423\pi\) | ||
0.976206 | − | 0.216845i | \(-0.0695766\pi\) | |||||||
\(674\) | 2.97111e13i | 0.213609i | ||||||||
\(675\) | − | 4.74091e12i | − | 0.0338332i | ||||||
\(676\) | −7.97090e13 | −0.564643 | ||||||||
\(677\) | − | 9.73601e12i | − | 0.0684601i | −0.999414 | − | 0.0342301i | \(-0.989102\pi\) | ||
0.999414 | − | 0.0342301i | \(-0.0108979\pi\) | |||||||
\(678\) | − | 9.80341e12i | − | 0.0684272i | ||||||
\(679\) | 6.46006e13i | 0.447598i | ||||||||
\(680\) | 3.66263e13 | 0.251912 | ||||||||
\(681\) | 4.80432e13 | 0.328017 | ||||||||
\(682\) | − | 8.84832e11i | − | 0.00599707i | ||||||
\(683\) | 7.39029e13 | 0.497231 | 0.248615 | − | 0.968602i | \(-0.420025\pi\) | ||||
0.248615 | + | 0.968602i | \(0.420025\pi\) | |||||||
\(684\) | − | 4.43737e13i | − | 0.296378i | ||||||
\(685\) | −2.49433e13 | −0.165387 | ||||||||
\(686\) | −2.66220e13 | −0.175235 | ||||||||
\(687\) | − | 3.20062e14i | − | 2.09146i | ||||||
\(688\) | 2.77256e13 | + | 1.37784e14i | 0.179862 | + | 0.893836i | ||||
\(689\) | −4.51022e13 | −0.290471 | ||||||||
\(690\) | − | 3.14999e13i | − | 0.201402i | ||||||
\(691\) | − | 2.93000e14i | − | 1.85985i | −0.367751 | − | 0.929924i | \(-0.619872\pi\) | ||
0.367751 | − | 0.929924i | \(-0.380128\pi\) | |||||||
\(692\) | 1.67551e13 | 0.105589 | ||||||||
\(693\) | − | 1.39267e13i | − | 0.0871326i | ||||||
\(694\) | −4.46569e13 | −0.277390 | ||||||||
\(695\) | − | 2.44819e14i | − | 1.50981i | ||||||
\(696\) | − | 4.01624e13i | − | 0.245908i | ||||||
\(697\) | −7.96025e13 | −0.483908 | ||||||||
\(698\) | 2.96952e13 | 0.179229 | ||||||||
\(699\) | 3.77567e14 | 2.26260 | ||||||||
\(700\) | − | 8.21349e12i | − | 0.0488694i | ||||||
\(701\) | 4.69230e13 | 0.277201 | 0.138601 | − | 0.990348i | \(-0.455740\pi\) | ||||
0.138601 | + | 0.990348i | \(0.455740\pi\) | |||||||
\(702\) | −1.25392e13 | −0.0735503 | ||||||||
\(703\) | −3.85655e13 | −0.224606 | ||||||||
\(704\) | 2.80073e13 | 0.161960 | ||||||||
\(705\) | −2.08629e14 | −1.19792 | ||||||||
\(706\) | 2.24088e13i | 0.127760i | ||||||||
\(707\) | 5.02690e13i | 0.284579i | ||||||||
\(708\) | − | 1.66917e14i | − | 0.938283i | ||||||
\(709\) | −9.97058e13 | −0.556531 | −0.278265 | − | 0.960504i | \(-0.589759\pi\) | ||||
−0.278265 | + | 0.960504i | \(0.589759\pi\) | |||||||
\(710\) | − | 3.82690e13i | − | 0.212107i | ||||||
\(711\) | −9.89266e13 | −0.544459 | ||||||||
\(712\) | 7.36182e13 | 0.402333 | ||||||||
\(713\) | 3.09236e13 | 0.167819 | ||||||||
\(714\) | − | 2.73967e13i | − | 0.147641i | ||||||
\(715\) | − | 2.42868e13i | − | 0.129969i | ||||||
\(716\) | 3.39056e13i | 0.180180i | ||||||||
\(717\) | 1.48932e14i | 0.785943i | ||||||||
\(718\) | − | 3.98025e13i | − | 0.208588i | ||||||
\(719\) | −1.78844e14 | −0.930741 | −0.465371 | − | 0.885116i | \(-0.654079\pi\) | ||||
−0.465371 | + | 0.885116i | \(0.654079\pi\) | |||||||
\(720\) | 8.18300e13i | 0.422912i | ||||||||
\(721\) | 2.94944e14i | 1.51378i | ||||||||
\(722\) | 1.84004e13i | 0.0937869i | ||||||||
\(723\) | 4.05471e14 | 2.05243 | ||||||||
\(724\) | −2.39311e14 | −1.20301 | ||||||||
\(725\) | − | 6.16982e12i | − | 0.0308022i | ||||||
\(726\) | 4.02861e13 | 0.199743 | ||||||||
\(727\) | − | 2.91641e14i | − | 1.43607i | −0.696005 | − | 0.718037i | \(-0.745041\pi\) | ||
0.696005 | − | 0.718037i | \(-0.254959\pi\) | |||||||
\(728\) | −4.41128e13 | −0.215729 | ||||||||
\(729\) | −4.75347e13 | −0.230873 | ||||||||
\(730\) | 1.04353e13i | 0.0503373i | ||||||||
\(731\) | 2.97893e13 | + | 1.48040e14i | 0.142716 | + | 0.709238i | ||||
\(732\) | −1.41722e13 | −0.0674346 | ||||||||
\(733\) | − | 2.10681e14i | − | 0.995648i | −0.867278 | − | 0.497824i | \(-0.834133\pi\) | ||
0.867278 | − | 0.497824i | \(-0.165867\pi\) | |||||||
\(734\) | 6.62755e13i | 0.311080i | ||||||||
\(735\) | 9.22999e12 | 0.0430293 | ||||||||
\(736\) | − | 1.01451e14i | − | 0.469748i | ||||||
\(737\) | 1.93105e13 | 0.0888087 | ||||||||
\(738\) | 1.14183e13i | 0.0521578i | ||||||||
\(739\) | 5.50708e13i | 0.249862i | 0.992165 | + | 0.124931i | \(0.0398709\pi\) | ||||
−0.992165 | + | 0.124931i | \(0.960129\pi\) | |||||||
\(740\) | 7.34364e13 | 0.330943 | ||||||||
\(741\) | −1.17539e14 | −0.526130 | ||||||||
\(742\) | 1.71101e13 | 0.0760734 | ||||||||
\(743\) | − | 5.59921e13i | − | 0.247276i | −0.992327 | − | 0.123638i | \(-0.960544\pi\) | ||
0.992327 | − | 0.123638i | \(-0.0394562\pi\) | |||||||
\(744\) | 1.65583e13 | 0.0726359 | ||||||||
\(745\) | 1.93946e14 | 0.845083 | ||||||||
\(746\) | −3.01185e13 | −0.130359 | ||||||||
\(747\) | −1.29927e14 | −0.558593 | ||||||||
\(748\) | 3.22241e13 | 0.137617 | ||||||||
\(749\) | 4.02900e14i | 1.70918i | ||||||||
\(750\) | 4.79512e13i | 0.202066i | ||||||||
\(751\) | 2.89087e14i | 1.21012i | 0.796179 | + | 0.605061i | \(0.206851\pi\) | ||||
−0.796179 | + | 0.605061i | \(0.793149\pi\) | |||||||
\(752\) | −2.12567e14 | −0.883908 | ||||||||
\(753\) | − | 1.22934e13i | − | 0.0507804i | ||||||
\(754\) | −1.63185e13 | −0.0669613 | ||||||||
\(755\) | −1.44092e14 | −0.587359 | ||||||||
\(756\) | −1.55355e14 | −0.629094 | ||||||||
\(757\) | 1.01995e14i | 0.410297i | 0.978731 | + | 0.205149i | \(0.0657678\pi\) | ||||
−0.978731 | + | 0.205149i | \(0.934232\pi\) | |||||||
\(758\) | 1.14947e13i | 0.0459359i | ||||||||
\(759\) | − | 5.62763e13i | − | 0.223417i | ||||||
\(760\) | 5.96118e13i | 0.235106i | ||||||||
\(761\) | 1.48371e14i | 0.581335i | 0.956824 | + | 0.290667i | \(0.0938773\pi\) | ||||
−0.956824 | + | 0.290667i | \(0.906123\pi\) | |||||||
\(762\) | 6.44511e13 | 0.250874 | ||||||||
\(763\) | − | 2.26484e14i | − | 0.875818i | ||||||
\(764\) | 1.21830e14i | 0.468045i | ||||||||
\(765\) | 8.79207e13i | 0.335571i | ||||||||
\(766\) | 3.54412e13 | 0.134389 | ||||||||
\(767\) | −1.37718e14 | −0.518816 | ||||||||
\(768\) | 2.30535e14i | 0.862839i | ||||||||
\(769\) | 4.82893e14 | 1.79564 | 0.897820 | − | 0.440362i | \(-0.145150\pi\) | ||||
0.897820 | + | 0.440362i | \(0.145150\pi\) | |||||||
\(770\) | 9.21349e12i | 0.0340385i | ||||||||
\(771\) | 1.50637e14 | 0.552919 | ||||||||
\(772\) | 3.37653e13 | 0.123136 | ||||||||
\(773\) | 4.77918e13i | 0.173163i | 0.996245 | + | 0.0865817i | \(0.0275943\pi\) | ||||
−0.996245 | + | 0.0865817i | \(0.972406\pi\) | |||||||
\(774\) | 2.12350e13 | − | 4.27301e12i | 0.0764448 | − | 0.0153826i | ||||
\(775\) | 2.54372e12 | 0.00909831 | ||||||||
\(776\) | 4.35385e13i | 0.154727i | ||||||||
\(777\) | − | 1.11544e14i | − | 0.393859i | ||||||
\(778\) | 3.44294e13 | 0.120790 | ||||||||
\(779\) | − | 1.29559e14i | − | 0.451626i | ||||||
\(780\) | 2.23819e14 | 0.775217 | ||||||||
\(781\) | − | 6.83698e13i | − | 0.235293i | ||||||
\(782\) | − | 3.44834e13i | − | 0.117917i | ||||||
\(783\) | −1.16700e14 | −0.396516 | ||||||||
\(784\) | 9.40423e12 | 0.0317499 | ||||||||
\(785\) | −3.65095e14 | −1.22478 | ||||||||
\(786\) | 6.97602e13i | 0.232539i | ||||||||
\(787\) | 2.33706e14 | 0.774098 | 0.387049 | − | 0.922059i | \(-0.373494\pi\) | ||||
0.387049 | + | 0.922059i | \(0.373494\pi\) | |||||||
\(788\) | −4.24793e13 | −0.139813 | ||||||||
\(789\) | 6.47047e14 | 2.11617 | ||||||||
\(790\) | 6.54471e13 | 0.212694 | ||||||||
\(791\) | −1.00212e14 | −0.323623 | ||||||||
\(792\) | − | 9.38607e12i | − | 0.0301202i | ||||||
\(793\) | 1.16931e13i | 0.0372874i | ||||||||
\(794\) | − | 1.68055e13i | − | 0.0532537i | ||||||
\(795\) | −1.76284e14 | −0.555108 | ||||||||
\(796\) | 3.21845e14i | 1.00712i | ||||||||
\(797\) | 3.00140e14 | 0.933325 | 0.466663 | − | 0.884435i | \(-0.345456\pi\) | ||||
0.466663 | + | 0.884435i | \(0.345456\pi\) | |||||||
\(798\) | 4.45900e13 | 0.137792 | ||||||||
\(799\) | −2.28389e14 | −0.701360 | ||||||||
\(800\) | − | 8.34513e12i | − | 0.0254673i | ||||||
\(801\) | 1.76719e14i | 0.535946i | ||||||||
\(802\) | − | 2.79174e13i | − | 0.0841400i | ||||||
\(803\) | 1.86432e13i | 0.0558398i | ||||||||
\(804\) | 1.77959e14i | 0.529711i | ||||||||
\(805\) | −3.21998e14 | −0.952520 | ||||||||
\(806\) | − | 6.72786e12i | − | 0.0197789i | ||||||
\(807\) | − | 1.75286e14i | − | 0.512130i | ||||||
\(808\) | 3.38795e13i | 0.0983740i | ||||||||
\(809\) | −2.84113e14 | −0.819877 | −0.409939 | − | 0.912113i | \(-0.634450\pi\) | ||||
−0.409939 | + | 0.912113i | \(0.634450\pi\) | |||||||
\(810\) | −7.68872e13 | −0.220510 | ||||||||
\(811\) | 2.70701e12i | 0.00771589i | 0.999993 | + | 0.00385794i | \(0.00122802\pi\) | ||||
−0.999993 | + | 0.00385794i | \(0.998772\pi\) | |||||||
\(812\) | −2.02179e14 | −0.572737 | ||||||||
\(813\) | − | 2.35135e14i | − | 0.662009i | ||||||
\(814\) | −4.01724e12 | −0.0112410 | ||||||||
\(815\) | −5.70267e14 | −1.58595 | ||||||||
\(816\) | 2.87595e14i | 0.794933i | ||||||||
\(817\) | −2.40945e14 | + | 4.84841e13i | −0.661924 | + | 0.133195i | ||||
\(818\) | −5.08185e13 | −0.138757 | ||||||||
\(819\) | − | 1.05892e14i | − | 0.287371i | ||||||
\(820\) | 2.46706e14i | 0.665441i | ||||||||
\(821\) | 2.40061e13 | 0.0643584 | 0.0321792 | − | 0.999482i | \(-0.489755\pi\) | ||||
0.0321792 | + | 0.999482i | \(0.489755\pi\) | |||||||
\(822\) | 1.25747e13i | 0.0335071i | ||||||||
\(823\) | −6.12116e14 | −1.62119 | −0.810597 | − | 0.585605i | \(-0.800857\pi\) | ||||
−0.810597 | + | 0.585605i | \(0.800857\pi\) | |||||||
\(824\) | 1.98782e14i | 0.523288i | ||||||||
\(825\) | − | 4.62919e12i | − | 0.0121125i | ||||||
\(826\) | 5.22449e13 | 0.135876 | ||||||||
\(827\) | −1.53725e14 | −0.397390 | −0.198695 | − | 0.980061i | \(-0.563670\pi\) | ||||
−0.198695 | + | 0.980061i | \(0.563670\pi\) | |||||||
\(828\) | 1.61542e14 | 0.415081 | ||||||||
\(829\) | − | 1.20932e14i | − | 0.308865i | −0.988003 | − | 0.154432i | \(-0.950645\pi\) | ||
0.988003 | − | 0.154432i | \(-0.0493549\pi\) | |||||||
\(830\) | 8.59559e13 | 0.218215 | ||||||||
\(831\) | 1.03969e14 | 0.262362 | ||||||||
\(832\) | 2.12955e14 | 0.534159 | ||||||||
\(833\) | 1.01042e13 | 0.0251928 | ||||||||
\(834\) | −1.23421e14 | −0.305885 | ||||||||
\(835\) | − | 3.33291e14i | − | 0.821091i | ||||||
\(836\) | 5.24470e13i | 0.128437i | ||||||||
\(837\) | − | 4.81134e13i | − | 0.117122i | ||||||
\(838\) | 1.02934e14 | 0.249079 | ||||||||
\(839\) | − | 1.74692e14i | − | 0.420206i | −0.977679 | − | 0.210103i | \(-0.932620\pi\) | ||
0.977679 | − | 0.210103i | \(-0.0673799\pi\) | |||||||
\(840\) | −1.72417e14 | −0.412271 | ||||||||
\(841\) | 2.68834e14 | 0.639006 | ||||||||
\(842\) | −4.73185e13 | −0.111807 | ||||||||
\(843\) | 2.65875e14i | 0.624510i | ||||||||
\(844\) | − | 2.62193e14i | − | 0.612221i | ||||||
\(845\) | 2.57047e14i | 0.596663i | ||||||||
\(846\) | 3.27604e13i | 0.0755957i | ||||||||
\(847\) | − | 4.11812e14i | − | 0.944675i | ||||||
\(848\) | −1.79612e14 | −0.409596 | ||||||||
\(849\) | − | 3.13149e14i | − | 0.709925i | ||||||
\(850\) | − | 2.83654e12i | − | 0.00639284i | ||||||
\(851\) | − | 1.40397e14i | − | 0.314564i | ||||||
\(852\) | 6.30073e14 | 1.40344 | ||||||||
\(853\) | 7.35089e13 | 0.162778 | 0.0813888 | − | 0.996682i | \(-0.474064\pi\) | ||||
0.0813888 | + | 0.996682i | \(0.474064\pi\) | |||||||
\(854\) | − | 4.43590e12i | − | 0.00976546i | ||||||
\(855\) | −1.43097e14 | −0.313185 | ||||||||
\(856\) | 2.71540e14i | 0.590834i | ||||||||
\(857\) | 5.75184e14 | 1.24423 | 0.622117 | − | 0.782924i | \(-0.286273\pi\) | ||||
0.622117 | + | 0.782924i | \(0.286273\pi\) | |||||||
\(858\) | −1.22437e13 | −0.0263315 | ||||||||
\(859\) | 9.34183e13i | 0.199741i | 0.995000 | + | 0.0998703i | \(0.0318428\pi\) | ||||
−0.995000 | + | 0.0998703i | \(0.968157\pi\) | |||||||
\(860\) | 4.58808e14 | − | 9.23235e13i | 0.975301 | − | 0.196255i | ||||
\(861\) | 3.74726e14 | 0.791950 | ||||||||
\(862\) | − | 1.48481e14i | − | 0.311985i | ||||||
\(863\) | 3.48918e14i | 0.728903i | 0.931222 | + | 0.364451i | \(0.118744\pi\) | ||||
−0.931222 | + | 0.364451i | \(0.881256\pi\) | |||||||
\(864\) | −1.57845e14 | −0.327840 | ||||||||
\(865\) | − | 5.40322e13i | − | 0.111576i | ||||||
\(866\) | −1.02818e14 | −0.211095 | ||||||||
\(867\) | − | 2.81387e14i | − | 0.574393i | ||||||
\(868\) | − | 8.33550e13i | − | 0.169174i | ||||||
\(869\) | 1.16925e14 | 0.235944 | ||||||||
\(870\) | −6.37816e13 | −0.127967 | ||||||||
\(871\) | 1.46828e14 | 0.292900 | ||||||||
\(872\) | − | 1.52642e14i | − | 0.302755i | ||||||
\(873\) | −1.04513e14 | −0.206111 | ||||||||
\(874\) | 5.61241e13 | 0.110050 | ||||||||
\(875\) | 4.90167e14 | 0.955662 | ||||||||
\(876\) | −1.71810e14 | −0.333063 | ||||||||
\(877\) | 9.14192e14 | 1.76214 | 0.881068 | − | 0.472989i | \(-0.156825\pi\) | ||||
0.881068 | + | 0.472989i | \(0.156825\pi\) | |||||||
\(878\) | − | 7.44138e13i | − | 0.142620i | ||||||
\(879\) | − | 9.30940e14i | − | 1.77410i | ||||||
\(880\) | − | 9.67180e13i | − | 0.183271i | ||||||
\(881\) | 6.90185e14 | 1.30043 | 0.650214 | − | 0.759751i | \(-0.274679\pi\) | ||||
0.650214 | + | 0.759751i | \(0.274679\pi\) | |||||||
\(882\) | − | 1.44936e12i | − | 0.00271540i | ||||||
\(883\) | −4.40508e14 | −0.820635 | −0.410317 | − | 0.911943i | \(-0.634582\pi\) | ||||
−0.410317 | + | 0.911943i | \(0.634582\pi\) | |||||||
\(884\) | 2.45018e14 | 0.453875 | ||||||||
\(885\) | −5.38276e14 | −0.991490 | ||||||||
\(886\) | − | 6.98615e13i | − | 0.127959i | ||||||
\(887\) | 1.15384e14i | 0.210149i | 0.994464 | + | 0.105074i | \(0.0335081\pi\) | ||||
−0.994464 | + | 0.105074i | \(0.966492\pi\) | |||||||
\(888\) | − | 7.51766e13i | − | 0.136150i | ||||||
\(889\) | − | 6.58832e14i | − | 1.18650i | ||||||
\(890\) | − | 1.16913e14i | − | 0.209369i | ||||||
\(891\) | −1.37363e14 | −0.244615 | ||||||||
\(892\) | 5.11229e14i | 0.905298i | ||||||||
\(893\) | − | 3.71719e14i | − | 0.654572i | ||||||
\(894\) | − | 9.77740e13i | − | 0.171213i | ||||||
\(895\) | 1.09339e14 | 0.190397 | ||||||||
\(896\) | −3.62622e14 | −0.627934 | ||||||||
\(897\) | − | 4.27900e14i | − | 0.736851i | ||||||
\(898\) | 1.16847e14 | 0.200094 | ||||||||
\(899\) | − | 6.26148e13i | − | 0.106630i | ||||||
\(900\) | 1.32881e13 | 0.0225035 | ||||||||
\(901\) | −1.92981e14 | −0.325005 | ||||||||
\(902\) | − | 1.34957e13i | − | 0.0226028i | ||||||
\(903\) | −1.40232e14 | − | 6.96892e14i | −0.233565 | − | 1.16072i | ||||
\(904\) | −6.75397e13 | −0.111871 | ||||||||
\(905\) | 7.71734e14i | 1.27123i | ||||||||
\(906\) | 7.26409e13i | 0.118998i | ||||||||
\(907\) | 2.81353e14 | 0.458369 | 0.229184 | − | 0.973383i | \(-0.426394\pi\) | ||||
0.229184 | + | 0.973383i | \(0.426394\pi\) | |||||||
\(908\) | − | 1.62999e14i | − | 0.264092i | ||||||
\(909\) | −8.13271e13 | −0.131044 | ||||||||
\(910\) | 7.00553e13i | 0.112262i | ||||||||
\(911\) | 7.11694e14i | 1.13423i | 0.823638 | + | 0.567116i | \(0.191941\pi\) | ||||
−0.823638 | + | 0.567116i | \(0.808059\pi\) | |||||||
\(912\) | −4.68081e14 | −0.741902 | ||||||||
\(913\) | 1.53565e14 | 0.242069 | ||||||||
\(914\) | 8.90871e13 | 0.139664 | ||||||||
\(915\) | 4.57028e13i | 0.0712586i | ||||||||
\(916\) | −1.08589e15 | −1.68387 | ||||||||
\(917\) | 7.13104e14 | 1.09978 | ||||||||
\(918\) | −5.36520e13 | −0.0822948 | ||||||||
\(919\) | −1.27393e15 | −1.94342 | −0.971712 | − | 0.236167i | \(-0.924109\pi\) | ||||
−0.971712 | + | 0.236167i | \(0.924109\pi\) | |||||||
\(920\) | −2.17015e14 | −0.329269 | ||||||||
\(921\) | − | 4.16679e13i | − | 0.0628788i | ||||||
\(922\) | 2.69498e12i | 0.00404484i | ||||||||
\(923\) | − | 5.19853e14i | − | 0.776019i | ||||||
\(924\) | −1.51694e14 | −0.225220 | ||||||||
\(925\) | − | 1.15488e13i | − | 0.0170540i | ||||||
\(926\) | −1.16442e14 | −0.171023 | ||||||||
\(927\) | −4.77172e14 | −0.697070 | ||||||||
\(928\) | −2.05419e14 | −0.298470 | ||||||||
\(929\) | − | 2.55612e14i | − | 0.369405i | −0.982794 | − | 0.184703i | \(-0.940868\pi\) | ||
0.982794 | − | 0.184703i | \(-0.0591322\pi\) | |||||||
\(930\) | − | 2.62961e13i | − | 0.0377987i | ||||||
\(931\) | 1.64453e13i | 0.0235122i | ||||||||
\(932\) | − | 1.28099e15i | − | 1.82166i | ||||||
\(933\) | 8.55823e14i | 1.21053i | ||||||||
\(934\) | 1.54755e14 | 0.217725 | ||||||||
\(935\) | − | 1.03917e14i | − | 0.145421i | ||||||
\(936\) | − | 7.13674e13i | − | 0.0993392i | ||||||
\(937\) | 8.48209e13i | 0.117437i | 0.998275 | + | 0.0587185i | \(0.0187014\pi\) | ||||
−0.998275 | + | 0.0587185i | \(0.981299\pi\) | |||||||
\(938\) | −5.57011e13 | −0.0767095 | ||||||||
\(939\) | 9.50498e13 | 0.130204 | ||||||||
\(940\) | 7.07827e14i | 0.964468i | ||||||||
\(941\) | 2.82807e14 | 0.383302 | 0.191651 | − | 0.981463i | \(-0.438616\pi\) | ||||
0.191651 | + | 0.981463i | \(0.438616\pi\) | |||||||
\(942\) | 1.84055e14i | 0.248138i | ||||||||
\(943\) | 4.71655e14 | 0.632508 | ||||||||
\(944\) | −5.48437e14 | −0.731589 | ||||||||
\(945\) | 5.00990e14i | 0.664768i | ||||||||
\(946\) | −2.50985e13 | + | 5.05043e12i | −0.0331277 | + | 0.00666611i | ||||
\(947\) | 4.44919e14 | 0.584159 | 0.292079 | − | 0.956394i | \(-0.405653\pi\) | ||||
0.292079 | + | 0.956394i | \(0.405653\pi\) | |||||||
\(948\) | 1.07754e15i | 1.40732i | ||||||||
\(949\) | 1.41755e14i | 0.184165i | ||||||||
\(950\) | 4.61666e12 | 0.00596637 | ||||||||
\(951\) | 1.74371e15i | 2.24167i | ||||||||
\(952\) | −1.88747e14 | −0.241377 | ||||||||
\(953\) | 6.91033e14i | 0.879092i | 0.898220 | + | 0.439546i | \(0.144861\pi\) | ||||
−0.898220 | + | 0.439546i | \(0.855139\pi\) | |||||||
\(954\) | 2.76814e13i | 0.0350305i | ||||||||
\(955\) | 3.92879e14 | 0.494586 | ||||||||
\(956\) | 5.05289e14 | 0.632777 | ||||||||
\(957\) | −1.13949e14 | −0.141956 | ||||||||
\(958\) | 1.44121e14i | 0.178608i | ||||||||
\(959\) | 1.28541e14 | 0.158470 | ||||||||
\(960\) | 8.32342e14 | 1.02081 | ||||||||
\(961\) | −7.93813e14 | −0.968504 | ||||||||
\(962\) | −3.05453e13 | −0.0370739 | ||||||||
\(963\) | −6.51828e14 | −0.787048 | ||||||||
\(964\) | − | 1.37567e15i | − | 1.65245i | ||||||
\(965\) | − | 1.08887e14i | − | 0.130118i | ||||||
\(966\) | 1.62329e14i | 0.192979i | ||||||||
\(967\) | 1.19497e15 | 1.41327 | 0.706637 | − | 0.707577i | \(-0.250212\pi\) | ||||
0.706637 | + | 0.707577i | \(0.250212\pi\) | |||||||
\(968\) | − | 2.77547e14i | − | 0.326557i | ||||||
\(969\) | −5.02921e14 | −0.588682 | ||||||||
\(970\) | 6.91433e13 | 0.0805177 | ||||||||
\(971\) | 1.50122e14 | 0.173919 | 0.0869596 | − | 0.996212i | \(-0.472285\pi\) | ||||
0.0869596 | + | 0.996212i | \(0.472285\pi\) | |||||||
\(972\) | − | 7.10317e14i | − | 0.818693i | ||||||
\(973\) | 1.26163e15i | 1.44667i | ||||||||
\(974\) | − | 1.54894e14i | − | 0.176702i | ||||||
\(975\) | − | 3.51982e13i | − | 0.0399483i | ||||||
\(976\) | 4.65656e13i | 0.0525794i | ||||||||
\(977\) | −3.65592e14 | −0.410699 | −0.205349 | − | 0.978689i | \(-0.565833\pi\) | ||||
−0.205349 | + | 0.978689i | \(0.565833\pi\) | |||||||
\(978\) | 2.87489e14i | 0.321312i | ||||||||
\(979\) | − | 2.08871e14i | − | 0.232255i | ||||||
\(980\) | − | 3.13151e13i | − | 0.0346437i | ||||||
\(981\) | 3.66414e14 | 0.403299 | ||||||||
\(982\) | −1.46387e14 | −0.160304 | ||||||||
\(983\) | − | 1.72397e15i | − | 1.87828i | −0.343531 | − | 0.939141i | \(-0.611623\pi\) | ||
0.343531 | − | 0.939141i | \(-0.388377\pi\) | |||||||
\(984\) | 2.52552e14 | 0.273763 | ||||||||
\(985\) | 1.36988e14i | 0.147741i | ||||||||
\(986\) | −6.98226e13 | −0.0749224 | ||||||||
\(987\) | 1.07513e15 | 1.14782 | ||||||||
\(988\) | 3.98783e14i | 0.423596i | ||||||||
\(989\) | −1.76505e14 | − | 8.77155e14i | −0.186542 | − | 0.927033i | ||||
\(990\) | −1.49060e13 | −0.0156741 | ||||||||
\(991\) | 1.52002e15i | 1.59030i | 0.606411 | + | 0.795151i | \(0.292609\pi\) | ||||
−0.606411 | + | 0.795151i | \(0.707391\pi\) | |||||||
\(992\) | − | 8.46911e13i | − | 0.0881616i | ||||||
\(993\) | −1.35150e15 | −1.39981 | ||||||||
\(994\) | 1.97213e14i | 0.203237i | ||||||||
\(995\) | 1.03789e15 | 1.06423 | ||||||||
\(996\) | 1.41520e15i | 1.44385i | ||||||||
\(997\) | 9.05181e14i | 0.918882i | 0.888208 | + | 0.459441i | \(0.151950\pi\) | ||||
−0.888208 | + | 0.459441i | \(0.848050\pi\) | |||||||
\(998\) | 2.76621e14 | 0.279404 | ||||||||
\(999\) | −2.18440e14 | −0.219536 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 43.11.b.b.42.19 | yes | 34 | |
43.42 | odd | 2 | inner | 43.11.b.b.42.16 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.11.b.b.42.16 | ✓ | 34 | 43.42 | odd | 2 | inner | |
43.11.b.b.42.19 | yes | 34 | 1.1 | even | 1 | trivial |